59. กำหนดให้ \(f(x)=\sqrt{2x+4}\) ค่าของ \(f^{\prime}(0)\) คือข้อใดต่อไปนี้

1. \(\frac{1}{4}\)
2. \(\frac{1}{2}\)
3. \(1\)
4. \(2\)

วิธีทำ ดิฟเลยครับ

\begin{array}{lcl}f(x)&=&\sqrt{2x+4}\\f(x)&=&(2x+4)^{\frac{1}{2}}\\f^{\prime}(x)&=&\frac{1}{2}(2x+4)^{\frac{1}{2}-1}\frac{d}{dx}(2x+4)\\&=&\frac{1}{2}(2x+4)^{-\frac{1}{2}}(2)\\&=&\frac{1}{(2x+4)^{\frac{1}{2}}}\\so\\f^{\prime}(0)&=&\frac{1}{(2(0)+4)^{\frac{1}{2}}}\\&=&\frac{1}{\sqrt{4}}\\&=&\frac{1}{2}\quad \underline{Ans}\end{array}